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What is the remainder when the positive integer x is divided

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Manager
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What is the remainder when the positive integer x is divided [#permalink] New post 26 Mar 2007, 22:24
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A
B
C
D
E

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What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.


In the decimal representation of x, where 0 < x < 1, what is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.


Favorable Unfavorable Not Sure
Candidate M 40 20 40
Candidate N 30 35 35

The table above shows the results of a survey of 100 voters each responded “favorableâ€
Director
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Re: 3 Q's: DS [#permalink] New post 27 Mar 2007, 02:21
[quote="GMAThopeful"]What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.


Statement 1 - possible values of x are 17, 29, 41, 53, 65....
remainder when x is divided by 8 are 1, 5, 1, 5, 1. So NOT suff

Statement 2 - possible values of x are 29, 47, 65,.......
remainder when x is divided by 8 are 5, 7, 1..... So NOT suff

Combining 1 and 2:
common numbers in statement 1 and 2 are 29, 65,.....
remainder when x is divided by 8 are 5,1 so NOT suff

Hence answer is 'E'
Director
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 [#permalink] New post 27 Mar 2007, 05:25
Answer should be 1) E, 2)
E, 3) C

1) E as explained

2) 16x is an integer so X can be any of these numbers 0.125 or 0.25 or 0.5
similarly 8x can be either 0.125 or 0.5 etc. by combining also we may not get the result. hence
E is the answer.

3) from set theory, lets say favorable for M is MF unfavourable for M is M
U, fav for N is NF unfavourable N is NU, while not sure for M and F are MS and NS.

putting the values we have 100 = MF + NF - (MF and NF) + UM + UN-(UM and UN) + MS + NS - (MS and NS)

from 1 will have 40 people have not voted in favour of either M or N. so from this can form another equation i.e.

40 = UM + UN - (UM and UN) + MS + NS - (MS and NS)

and from 2 we have ( UM and UN) = 10

not putting the values will get (MS + NS)

subsituting these valuse in first equation we may know the value of (MF+NF)

hence answer is C.

neither of 1 or 2 is sufficient by its own.

regards,

Amardeep
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Q3 [#permalink] New post 27 Mar 2007, 07:08
how does the forum rate Q3?

in which category would Q3 fall? simple/intermediate/difficult?

I ask this coz I was stumped by Q3
Director
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 [#permalink] New post 27 Mar 2007, 15:50
In the decimal representation of x, where 0 < x < 1, what is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

I agree with Amardeep.
Is there any method other than plug-in numbers.
  [#permalink] 27 Mar 2007, 15:50
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